Visualizing N-dimensional parameter spaces is a major challenge, even for relatively simple optical systems with just two or three lenses. These spaces are filled with numerous local minima, forming a complex landscape of hills and valleys shaped by the system’s design variables. A common mistake is to draw oversimplified conclusions from basic cases and assume that more complex systems behave like higher-dimensional versions of the same landscape. In reality, this assumption often breaks down.

In practical optical designs, the merit function becomes far more intricate. The resulting parameter landscape contains fine structural details and subtle irregularities. For example, what seems like the peak of a mountain may hide local dips that trap the design in highly suboptimal minima. Both local and global optimization strategies can only probe a limited portion of this high-dimensional space, constrained by finite time and computational resources. And this challenge intensifies when real-world constraints such as manufacturability, tolerances, and costs are added on top of the nominal design variables. This is precisely where our ‘First Time Right’ approach introduces a fundamental shift in methodology.

At the heart of our proprietary ‘First Time Right’ methodology is a radical reduction in parameter space dimensionality. Using fully analytic calculations, we determine the surface shapes that minimize and balance all aberrations by order. This reduces the initial N-dimensional design space to a much smaller, more manageable subspace. As a result, both local and global optimization methods, as well as machine learning tools can operate far more efficiently. This enables a deeper and more targeted exploration of the design space. Moreover, with fewer parameters to manage, we can account for real-world constraints, tolerances, and cost factors right from the start.